Britain's rental market is "overheating" with a third of tenants in the south-east and London paying more than 50% of their take-home pay to landlords, according to property website Rightmove.

Average rents continue to spiral upwards, with the monthly cost of a typical flat in the capital jumping 2.3% in August alone, and 5.8% over a year, to a record £1,272, according to separate figures from HomeLet, a tenant referencing service.

Fears are growing for a new generation of "trapped renters", squeezed by flat incomes and rising rents which make it virtually impossible to save for a deposit on a new home.

"These 'trapped renters' are faced with the prospect of a downward spiral where spending more income on rent also means saving less for a deposit," said Miles Shipside, director of Rightmove, which estimates that 31% of tenants in the south-east and 29% in London are already spending more than half their take-home pay on rent.

Last week the government promised £300m in funding for 15,000 homes for first-time buyers, but at the same time relaxed rules on builders who complain sites are not profitable if they are forced to build affordable homes.

But the lack of finance for young borrowers, particularly those unable to save for a large deposit, plus the generally high level of house prices, remains the nub of the issue. The Financial Services Authority said yesterday that new lending for house purchases continued to stagnate at about £40bn in the second quarter of 2012 – the same level as last year.

Only a tiny proportion of lending is going to those with small deposits or who need a large multiple of their salary to afford a home. The FSA said just 2% of mortgages were granted to buyers with a deposit of 10% or less. It added: "New lending with a combination of high LTV [loan to value] and high income multiple was unchanged from the previous quarter, slightly in excess of 1% of new lending."

The FSA also noted that the average interest rate on a new mortgage, including both house movers as well as first-time buyers, rose from 3.5% to 3.78% in the second quarter of 2012 despite the Bank of England base rate remaining at 0.5%.

Last month, the government's Funding for Lending scheme began, aimed at driving down the cost of loans for businesses and homebuyers, but so far there is little evidence of falling rates.

Housing analysts reckon tenants in many parts of the country are hitting the limits on how much more they can afford to pay. HomeLet, which examines tenant's incomes to check they can afford to pay, found average earnings were down 0.1% on a year ago. "Tenants are being stretched more than ever, and it will be interesting to see how long they'll be able to afford these continually rising living costs," said Ian Fraser, managing director of HomeLet.

Meanwhile, landlords are enjoying bumper incomes as tenants struggle. Rightmove estimated the "yield" on investment properties is now running at an average of 6% across the UK, or more than double the amount investors can typically earn on a savings account.

But the national average rental figures mask huge regional variations. HomeLet said the average rental home outside the capital costs about £684 a month, an increase of 1.9% on the year.

Rents are lowest in the north-east where they average £524 a month and have been falling for three years, HomeLet said.